What steps are required form an algorithm to convert a binary number to it's decimal equivalent?

Answer 1

Let's look at an example. If you want to convert the number 100112 to decimal you can split up the number so each digit has an index associated to it:

4 3 2 1 0

1 0 0 1 1

We can then find the decimal value:

24 * 1 + 23 * 0 + 22 * 0 + 21 * 1 + 20 * 1 =

16 * 1 + 8 * 0 + 4 * 0 + 2 * 1 + 1 * 1 = 16 + 0 + 0 + 2 + 1 = 19

So what we need to do is to multiply each of the binary digits by the value of two raised to the index of the digit. This will give you the conversion from any binary number to a decimal number.

Answer 2

Take the number you wish to convert to binary and divide it by two over and over again - keeping the remainder of each division. Your first division's remainder will be the least significant bit and the last division's remainder will by the most significant bit.

Example: Convert 13 to a binary number:

13/2 = 6 R 1 (least significant bit)

6/2 = 3 R 0

3/2 = 1 R 1

1/2 = 0 R 1 (most significant bit)

Thus 13 = 1101

Example: Convert 1,352 to a binary number:

1352/2 = 676 R 0 (least significant bit)

676/2 = 338 R 0

338/2 = 169 R 0

169/2 = 84 R 1

84/2 = 42 R 0

42/2 = 21 R 0

21/2 = 10 R 1

10/2 = 5 R 0

5/2 = 2 R1

2/2 = 1 R0

1/2 = 0 R1 (most significant bit)

Thus 1352 =

101 0100 1000

Notice that you most significant bit will ALWAYS be a 1 (since 0101 = 101).

Answer 3

Multiply the right-most digit by 1, the second digit from the right by 2, the next by 4, etc. and add up all the results.

Answer 4

an algorithm that converts a decimal number to Binary Coded Decimal (BCD) representation.

Answer 5

with hexidecimal you neednt use as many chartictors to represent a number. in binary 15 would be 01111 where as in hex it would be E resulting in much quicker coding times